Maximum Principle in the Optimal Design of Plates with StratifiedThickness

An optimal design problem for a plate governed by a linear, ellipticequation with bounded thickness varying only in a single prescribeddirection and with unilateral isoperimetrical-type constraints isconsidered. Using Murat–Tartars homogenization theory for stratifiedplates and Young-measure relaxation theory, smoothness of the extended cost and constraint functionals is proved, and then the maximum principlenecessary for an optimal relaxed design is derived.